The atom-bond sum-connectivity (ABS) index is a recently introduced variant of three earlier much-studied graph-based molecular descriptors: Randić, atom-bond connectivity, and sum-connectivity indices. The general atom-bond sum-connectivity index is defined as ABSα(G) = ∑ uv∈E(G) ( du+dv−2 du+dv )α , where α is a real number. In this paper, we present some upper and lower bounds on the general atom-bond sum-connectivity index in terms of graph parameters and other graph indices.